Introduction to Experimental Electrochemistry

Transcription

1 Introduction to Experimental Electrochemistry Teacher Edition Cynthia A. Schroll Stephen M. Cohen

2 2 XXBasic equations Nernst equation E = Ec - b RT l nf ln Q E = n log Q at 25cC Cottrell equation it () = nfac D rt Levich equation = il nFAD ~ o C Randles-Ševćik equation nf D ip = o nFAC RT ip = ] # 10 gn y D AC at 25cC XXPhysical constants (2014 CODATA Recommended Values) c Speed of light in vacuum m s 1 e Elementary charge C F Faraday constant C mol 1 h Planck constant J s k Boltzmann constant J K 1 N A Avogadro constant x mol 1 R Molar gas constant J mol 1 K 1 f0 Permittivity of free space F m 1 or C 2 N 1 m 2 Gamry Instruments, Inc.

3 3 Introduction to Experimental Electrochemistry Teacher s Guide

4 4 Gamry Instruments, Inc.

5 5 Introduction to Experimental Electrochemistry Teacher s Guide Cynthia A. Schroll Stephen M. Cohen Gamry Instruments, Inc. Warminster, Pennsylvania

6 6 Copyright 2016 by Gamry Instruments, Inc. All rights reserved. Printed in the United States of America. No part of this book may be reprinted, transmitted, reproduced, or used in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without permission in writing from Gamry Instruments, Inc. Neither Gamry Instruments, Inc., its officers, directors, nor its employees accept responsibility for the use of methods and materials discussed herein. No authorization is implied concerning the use of patented or copyrighted material. The information is advisory only and the use of the materials and methods is solely at the risk of the user. Gamry, Interface 1000, Analyst, and Framework are trademarks of Gamry Instruments, Inc. Trademark notice: Other product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Gamry Instruments, Inc., 734 Louis Drive, Warminster, Pennsylvania Gamry Instruments Part Number ISBN-10: ISBN-13: Gamry Instruments, Inc.

7 7 Contents Foreword 13 Introduction 15 Basic Theory 15 Major Techniques 18 Experimental Apparatus 25 Basic Set-up 25 The Potentiostat 25 The Electrochemical Cell 26 Electrical Shielding 37 Calibrating the Potentiostat 38 Materials Available from Gamry Instruments 39 Non-Gamry Materials Required 40 A Word on Statistics 41 Mean 41 Standard Deviation 41 Relative Standard Deviation 41 Cyclic Voltammetry 43 Goals 43 Experimental Apparatus 43 Reagents and Chemicals 43 Background 44 Procedure 47 Reference 50 Data Analysis 51 Hints and comments for the teacher s guide are shown in reddish-brown. Page numbers in the teacher s guide may vary slightly from the student edition.

8 8 Questions 53 Common Problems 54 Determination of the Working Area of an Electrode 55 Goals 55 Experimental Apparatus 55 Reagents and Chemicals 55 Background 56 Procedure 59 References 65 Data Analysis 67 Results 68 Questions 70 Common Problems 70 Comparison of Pulse Techniques 71 Goals 71 Experimental Apparatus 71 Reagents and Chemicals 71 Background 72 Procedure 75 References 80 Data analysis 81 Results 81 Questions 83 Common Problems 84 Gamry Instruments, Inc.

9 9 Quantitative Determination of Ions by Stripping Voltammetry 85 Goals 85 Experimental Apparatus 85 Reagents and Chemicals 85 Background 86 Procedure 87 Reference 91 Data Analysis 93 Results 93 Questions 96 Common Problems 96 Determination of Acetaminophen 97 Goal 97 Experimental apparatus 97 Reagents and chemicals 97 Background 97 Procedure 99 Reference 103 Data Analysis 105 Results 106 Questions 108 Common Problems 110 Simulations of Cyclic Voltammetry Data 111 Goals 111 Experimental Apparatus 111

10 10 Introduction 111 Procedure 117 References 127 Data Analysis 129 Results 130 Common Problems 134 Microelectrodes 135 Goals 135 Experimental Apparatus 135 Reagents and Chemicals 135 Background 135 Procedure 137 Reference 141 Data Analysis 143 Questions 146 Common Problems 146 Detection of Glucose in a Carbonated Beverage 147 Goals 147 Experimental Apparatus 147 Reagents and Chemicals 147 Safety Warning 148 Background 148 Procedure 149 Reference 153 Data Analysis 155 Gamry Instruments, Inc.

11 11 Results 156 Questions 158 Common Problems 159 Electrochemical Polymerization of a Monomer 161 Goals 161 Experimental Apparatus 161 Reagents and Chemicals 161 Background 162 Procedure 163 Reference 168 Data Analysis 169 Results 170 Questions 171 Common Problems 171 Electrochemical Impedance Spectroscopy 173 Goals 173 Experimental Apparatus 173 Background 173 Procedure 177 Reference 181 Data Analysis 183 Results 186 Questions 186 Common Problems 187

12 12 Corrosion of Mild Steel at different phs 189 Goals 189 Experimental Apparatus 189 Reagents and Chemicals 189 Introduction 190 Procedure 193 References 203 Data Analysis 205 Results 206 Questions 207 Common Problems 207 Gamry Instruments, Inc.

13 13 Foreword I have been so electrically occupied of late that I feel as if hungry for a little chemistry: but then the conviction crosses my mind that these things hang together under one law & that the more haste we make onwards each in his own path the sooner we shall arrive, and meet each other, at that state of knowledge of natural causes from which all varieties of effects may be understood & enjoyed. Michael Faraday, 1838 Electrochemistry often gets short shrift in modern undergraduate chemistry curricula. A student sees the Nernst equation in first-year General Chemistry, and revisits it during a discussion of thermodynamics in Physical Chemistry but there the topic rests. Yet the modern technological world is driven by electrochemistry, in the form of compact batteries for the myriad of portable electronic devices, and more and more in the form of powerful electric batteries to run our cars. How to prevent or minimize corrosion of metals has been a crucial subject for engineers for centuries. Conversion and storage of electrical energy is an active research topic for energy conservation. Even biology and neuroscience is very much a subject of ionic gradients across cell membranes. In fact, one of the most common consumer medical devices the glucose meter is based on an electrochemical measurement. Thus every scientist and engineer must know some basics about our truly electrochemical world. This book is an attempt to introduce the undergraduate, in one semester, to some of the present-day techniques found in modern electrochemistry and electroanalytical chemistry. We assume that the student has had one full year of General Chemistry lecture and laboratory. Organic Chemistry and Physical Chemistry are decidedly helpful, but not required. The laboratory experiments are designed to be run in the order presented in this book. All data-collection, analysis, and questions are on separate pages from the background and procedure; they may be torn out from the book and handed in with graphs and plots that the student generates. Occasionally we offer a Bonus Question to give the student a deeper consideration of the techniques and theory. All of the specialized electrochemical instrumentation mentioned herein may be purchased from Gamry Instruments, Inc. in order to set up a complete electro-

14 14 Foreword chemistry laboratory. Contact Gamry at (toll-free in the USA and Canada), fax us at , send us an at or contact your local distributor, for more information. Gamry Instruments, Inc.

15 Basic Theory 15 Introduction From your chemical education, you should be familiar with certain electrochemical ideas already. These basic ideas include Half-reactions, Formal potentials, Reference electrodes, The Nernst equation, Free-energy calculations, Simple dual-electrode cells. This laboratory manual deals with potentiostatic and galvanostatic methods. Techniques where the potential of an electrode is the controlled variable, while the current is measured are called potentiostatic methods. Galvanostatic methods reverse the situation (current is controlled, while voltage is measured). XXBasic Theory Nernst Equation The Nernst equation describes a relationship between electrode potential and solution concentration: E = Ec - b RT l nf ln Q Here Q is the reaction quotient is the product of the activity times concentration for the products divided by the product of the activity times concentration for the reactants. At room temperature (25 C = 298 K), using the Ideal Gas Constant and base-10 logarithms, RT / F = V, so the Nernst equation becomes. V E = Ec n log Q The Nernst equation is used for predicting the concentrations of species near the electrode surface at a given applied potential. The Nernst equation is relatively accurate only when the electrochemical system responds quickly to changes in the ap- Walther Nernst ( ), physicist, derived his relationship in In most cases (when concentrations of species are not too high), you may use concentrations instead of activities.

16 16 Introduction Michael Faraday ( ), physicist and chemist, was active in electrochemical research around This Q is not the same as the reaction quotient Q. 1 F = C = A s plied potential. Such redox systems remain in quasi-equilibrium with the electrode surface. These systems sometimes are known as Nernstian or reversible systems because they are in quasi-equilibrium. The potential of the working electrode determines what kind of redox processes may occur at the electrode s surface. Extremely negative potentials will probably reduce analytes while positive potentials are likely to oxidize them. Should oxidation or reduction happen, a current flows through the electrode, and the magnitude of this current is proportional to concentrations in the solution. Thus, the current gives the detectable signal that can be used as a calibration curve relating signal to concentration. Heterogeneous States Electrochemical systems must be heterogeneous. Worthwhile chemical and electrochemical reactions occur at or near the surface of the working electrode. This means that the electrode affects the volume of solution close to the electrode. In general, the electrode influences a volume of solution extending just a few micrometers away from the surface of the electrode. Concentrations of analyte in this very local diffusion layer can vary dramatically from those measured in the rest of the solution. The volume of the diffusion layer is tiny compared to the total amount of solution in the electrochemical cell. Hence any changes in concentration in the diffusion layer created by the electrode rarely influence the bulk solution. Faraday s Law Faraday s Law states that the amount of charge in an electrochemical process is directly proportional to the underlying stoichiometry of that half-reaction. Most half-reactions involve simple transfers of one electron, therefore application of Faraday s Law leads to the general statement that, for every mole of a species that is oxidized or reduced at an electrode, a mole of electrons (with a charge Q of coulombs) enters or leaves the electrode. where m = mass, Q = charge, M = molar mass, F = Faraday s constant, and z = valence number. m QM = Fz Gamry Instruments, Inc.

17 Basic Theory 17 For half-reactions requiring two, three, or four electrons, Q, the quantity C/ mol, is multiplied by the corresponding whole number. Faraday s Law is integral, for it describes the connection between the observed current and concentration of the species. Generally higher concentrations give higher currents. When the electrode potential is perturbed far enough from its equilibrium value, the current is limited solely by how fast the analyte can diffuse to the surface of the electrode. For solutions that are not stirred, the analyte must diffuse passively across the diffusion layer from the bulk solution to the surface of the electrode. The diffusion rate is governed by a concentration gradient that is, diffusion transfers material from a volume of high concentration to one of low concentration. Not only that, but the larger the difference between the two concentrations, the faster the species diffuses. (This is similar to the behavior of gases.) Therefore the current at an electrode is highestwhen the gradient in concentration of analyte across the diffusion layer is highest. Fick s First Law of Diffusion We need to describe diffusion of atoms, molecules, and ions, and so we add Fick s First Law of Diffusion: j] J =- D jx This equation describes diffusion (under steady-state conditions) in terms of flux J (amount of substance flowing through a given area during a given time), that is, diffusion occurs from high concentration to low concentration. When we combine Faraday s Law with Fick s First Law of Diffusion, we obtain a general expression for the diffusion-limited current, i d, at a working electrode, dc id = nfadb l dx 0 where n is the number of electrons involved in the half-reaction, F is Faraday s constant ( C/mol) A is the electrode area in cm 2, D is the analyte s diffusion coefficient, in cm 2 /s, and (dc/dx) 0 is the concentration gradient at the surface of the electrode. This expression may be new to you. The key point of this combined expression is the direct proportion between current and concentration gradient. Technically the current at higher potentials is not related to how fast analyte diffuses to the electrode surface, but rather how the energy states overlap. Very large overpotentials will actually see a decrease in current. Adolf Fick ( ), physiologist, derived his laws of diffusion in 1855.

18 Materials Available from Gamry Instruments 39 XXMaterials Available from Gamry Instruments Below is a table of all materials Gamry Instruments supplies in a complete electrochemistry course kit to perform all eleven experiments for ten pairs of students. Part number Description Quantity Sample of mild steel Ag AgCl reference electrode Platinum working electrode Platinum microlectrode Micro stirring bar Carbon screen-printed electrode Platinum screen-printed electrode Cuvette cap DigiElch student edition Student edition book Teacher edition book Dr. Bob s Cell kit Polishing kit EuroCell kit AC Dummy Cell Screen-printed electrode cell stand for 4 mm banana plugs Screen-printed electrode adapter for 4 mm cable 1

19 40 Experimental Apparatus XXNon-Gamry Materials Required Below is a table of all materials Gamry Instruments does not supply but are required to perform all eleven experiments for ten pairs of students. All chemicals should be 95+% pure. Material Quantity 1000 ppm std aqueous Cu with 2% w/w HNO ml 1000 ppm std aqueous Pb with 2% w/w HNO ml 3-methylthiophene (monomer) 2 ml / 2 g acetaminophen (paracetamol) elixir 8 fl. oz. or 250 ml acetaminophen (paracetamol) tablet 1 bottle of 50 tablets acetaminophen (paracetamol) 7 g acetonitrile 275 ml citric acid 20 g dialysis membrane 1 package disposable cuvette, 4.5 ml capacity 1 ferrocene 1 g glucose 5 g glucose oxidase, from Aspergillus niger, Type II, units 000 units/g solid (no added oxygen) perchloric acid 5 ml potassium chloride 44 g potassium ferricyanide 1 g pyrocatechol 1 g sodium phosphate dibasic heptahydrate 5 g sodium phosphate monobasic monohydrate 8 g sodium sulfate 3 g sulfuric acid 140 ml tetrabutylammonium hexafluorophosphate 10 g tetrabutylammonium tetrafluoroborate 4 g PTFE tubing (L O.D. I.D.) 10 ft ¹/16 in in.* 1 package * This is the tubing that fits into the cap of the SPE cuvette cell. You also must supply your own fittings to connect this tubing to your in-house nitrogen-system outlet. Gamry Instruments, Inc.

20 Goals 43 Cyclic Voltammetry XXGoals The goals of this experiment are to: Learn how to set up a screen-printed electrode Learn how to operate the Gamry potentiostat Determine the redox potential of potassium ferricyanide Calculate the diffusion coefficient of potassium ferricyanide XXExperimental Apparatus Gamry Instruments Interface 1000T Gamry Instruments Framework software package installed on a host computer Screen-printed electrode (SPE) cell stand (Gamry part number ) Platinum working screen-printed electrode (Gamry part number ) XXReagents and Chemicals Solution Preparation 0.1 M KCl Weigh out 0.74 g KCl for every 100 ml of water needed. 100 ml of solution provides aliquots of 1 ml each. 2 mm potassium ferricyanide in 0.1 M KCl Weigh out 0.74 g KCl and 0.06 g potassium ferricyanide for every 100 ml of water needed. 100 ml of solution provides aliquots of 1 ml each. Solution Purging 1. Purge both solutions with an inert gas (preferably N 2 ) for 10 min. 2. Blanket each solution with the inert gas. 3. Stopper immediately. The laboratory instructor has already purged the solutions of dissolved O 2. Purging the dissolved O 2 from these solutions prevents spurious peaks from appearing in your data. CAUTION: Cyanide-containing compounds can hydrolyze to form hydrogen cyanide gas, which is highly poisonous. Never pour potassium ferricyanide down the drain!

21 44 Cyclic Voltammetry XXBackground Cyclic voltammetry is the most commonly used electroanalytical technique for obtaining rapid quantitative data about an electrochemical reaction. The importance of cyclic voltammetry is that it provides a quick result concerning the kinetics of a heterogeneous electron-transfer, diffusion coefficients, and thermodynamic information for a process. Cyclic voltammetry also can give data on subsequent chemical reactions or adsorption processes. Cyclic voltammetry is usually the first experiment performed on an electroactive analyte because of its ability to provide the redox potential of that analyte. This technique also allows fast evaluation of the effect that a particular matrix may have on a redox process. During a typical cyclic voltammetry experiment, a component of the solution is electrolyzed (oxidized or reduced) by placing the solution in contact with an electrode, and then applying a potential to that electrode that is sufficiently positive or negative with respect to a reference half-cell (e.g., calomel or Ag AgCl). The electrode s voltage is adjusted higher or lower linearly, and finally, the voltage is returned to the original value at the same linear rate. Figure 1.1. A generic CV. A CV plot reveals the reversibility of the redox couple. (Adapted from P. T. Kissinger and W. R. Heineman, Laboratory Techniques in Electroanalytical Chemistry, New York: Marcel Dekker, Inc., 1984, p. 88.) Gamry Instruments, Inc.

22 Background 45 When the electrode becomes sufficiently negative or positive, a species in solution may gain electrons from the electrode s surface, or transfer electrons to that surface. As the potential is swept back and forth past the formal potential, E, of an analyte, a current flows through the electrode that either oxidizes or reduces the analyte. Electron-transfer is a measurable current in the electrode s circuitry. The magnitude of this current is proportional to the concentration of the analyte in solution, which allows cyclic voltammetry to be used in an analytical determination of concentration. The result is a cyclic voltammogram (or CV), in the form of a cycle between current and potential, where potential is plotted on the x-axis, and current is plotted on the y-axis. Figure 1.1 shows a generic cyclic voltammogram. The potential is graphed along the x-axis with more positive (or oxidizing) potentials plotted to the right, and more negative (or reducing) potentials to the left. The current is graphed on the y-axis of the voltammogram, with cathodic (i.e., reducing) currents plotted in the negative direction, and anodic (i.e., oxidizing) currents plotted in the positive direction. The peaks in a voltammogram look something like those in a spectrum or chromatogram. Each peak denotes a particular electrolytic process in the analytical solution, and the height of a peak is proportional to the concentration of that analyte. The peaks in a cyclic voltammogram are asymmetrical, with the leading side steep and the trailing side showing a gradual fall-off. The peaks seen during the reverse scan have the same overall form as those in the forward sweep, but they are inverted because the current is flowing in the opposite direction. The initial direction of the first sweep in a cyclic voltammetry experiment may be in either the positive (anodic) or negative (cathodic) direction, as determined by the characteristics of the analyte. For an oxidizable analyte, the first sweep starts in the positive direction, whereas for a reducible analyte, the first sweep begins in the negative direction. Much quantitative information can be extracted from a high-quality cyclic voltammogram. First, the plot can serve as a test if a redox couple is actually electrochemically reversible. The peak potential for the anodic sweep, E pa, and the peak potential for the cathodic peak, E pc, can be read right from the voltammogram, and the difference between them, E peak, can be calculated. If the redox couple is reversible, then, based on the Nernst equation, E = E (RT/nF) log[ox/red], the relationship between the ΔE peak and the number of electrons involved in the redox couple is nd Epeak = 59 mv (1.1)

23 46 Cyclic Voltammetry where n is the number of electrons taking part in the redox couple. In fact, for this particular experiment, ferricyanide ion undergoes a reversible one-electron transfer according to the following reaction: Fe(CN) 6 3 (aq) + e Fe(CN) 6 4 (aq) (1.2) The anodic peak current i pa is equal to the cathodic peak current i pc, so that the relationship, i i pc pa = 1 also holds true. A ratio of the peak currents deviating from 1 is an indication of chemical or electrochemical irreversibly. If the ratio is <1 but a return peak is present, then the electrochemical reaction is said to be pseudo-reversible. The peak currents are not measured using the x-axis as a baseline. Rather, you must first extrapolate a background current baseline out to the peak potential (see Figure 1.1). Then, the peak current is measured vertically from the peak down to the extrapo- nf D ip = o nFAC (1.4) RT lated baseline. The formal potential, E, for a reversible redox couple is easily found as the average of the two peak potentials: Epa + Epc E = (1.5) c 2 Quantitative information about concentration of the analyte can be determined from the voltammogram via the Randles-Ševćik equation (Eqn. 1.5). This equation calculates the peak current, i p (either anodic or cathodic), in terms of the concentration C of the analyte. In this equation, n is the number of electrons appearing in half-reaction for the redox pair, v is the scan-rate for the potential sweep (V/s), F is Faraday s constant ( C/mol), A is the electrode area (cm 2 ), R is the gas constant (8.314 J mol 1 K 1 ), T is the absolute temperature (K), and (1.3) Gamry Instruments, Inc.

24 Procedure 47 D is the diffusion coefficient of the analyte(cm2/s). If we assume standard temperature (25 C, K), the Randles-Ševćik equation can be written concisely as 3 2 i p = # 105 n AC y D (1.6) where the constant has units of C mol 1 V 1/2. The peak current is directly proportional to the concentration of the analyte. If the analyte concentration is known, then cyclic voltammetry can be used to find the analyte s diffusion coefficient. The diffusion coefficient shows how fast the analyte moves through the solution because of random collisions with other molecules. XXProcedure NOTE: Ensure that all glassware is as clean as possible. The solvents and reagents used to make solutions should be as pure as possible. We recommend that you use deionized, ultrafiltered (DIUF) water, conductivity water, or HPLC-grade water for the final rinsing of glassware and to prepare all solutions. Prepare the cell. 4. Connect the banana pins for the green (working), blue (working sense), white (reference), red (counter), and orange (counter sense) to the banana jacks indicated on the SPE cell stand. Leave the black (ground) pin unconnected. 5. Insert the screen-printed electrode horizontally into the connector on the SPE cell stand. The apparatus should be set up like that shown in Figure 1.2. Screen-printed electrode Figure 1.2. Left: Screen-printed electrode inserted into SPE cell stand. Right: Complete set-up. Lab Book with SPE teacher.indd 47 12/13/ :21:26 AM

25 48 Cyclic Voltammetry NOTE: When you add a drop of reagent, you only need enough to completely cover all three electrodes on the face of the screen-printed electrode. More reagent is unncessary. Perform a background scan. 1. Turn on the potentiostat, and, on the host computer s Windows desktop, open the Gamry Framework software. 2. When the host computer detects the potentiostat, choose Experiment > Physical Electrochemistry > Cyclic Voltammetry. The Cyclic Voltammetry window opens. Figure 1.3. Cyclic Voltammetry window, with fields set to run a blank. Gamry Instruments, Inc.

26 Procedure 49 Figure 1.4. Single drop of fluid on the SPE s electrodes. 3. Set the experimental fields in the Cyclic Voltammetry window to those shown in Figure 1.3, with the file name as blank. 4. Place a drop of the blank solution, 0.1 M KCl, onto the electrodes of the SPE. (See Fig. 1.4.) 5. Click the OK button to run the experiment. Perform scans using sample solution. 1. Rinse the SPE with de-ionized water into a waste container. Then dab the SPE with a laboratory wiper to remove the rinsing solution. NOTE: Do not get water on the SPE board. 2. Place a drop of the 2 mm potassium ferricyanide in 0.1 M potassium chloride solution onto the screen-printed electrode (Fig. 1.4). 3. In the experimental window, change the file name to FeCN6 10mVs-1.dta. 4. Run the experiment. 5. Redo steps 1 through 4, changing the scan rate to 20 mv/s and the file name to FeCN6 20mVs-1.dta. 6. Redo steps 1 through 4, this time changing the scan rate to 30 mv/s, then 40, 50, 60, 70, 80, 90, and 100 mv/s, simultaneously adjusting the file name appropriately. 7. Remove the screen-printed electrode from the connector, and discard it in the waste can. 8. Discard the analyte solution into the appropriate waste container (NEVER DOWN THE DRAIN!). Lab Book with SPE teacher.indd 49 12/13/ :21:29 AM

27 50 Cyclic Voltammetry X X Reference J.J. van Benschoten, J.Y. Lewis, W.R. Heineman, D.A. Roston, and P.T. Kissinger, J. Chem. Ed., 1983, 60(9), 772. Gamry Instruments, Inc.

28 Data Analysis 51 XXData Analysis Determine cathodic and anodic peak currents and voltages. 1. On the host computer s desktop, open Gamry Echem Analyst software. 2. Use Echem Analyst to determine the potential of cathodic and anodic peaks and cathodic and anodic peak currents. a. Open the CV file you want to evaluate. b. Using the mouse icon, select the region for the peak, and choose Cyclic Voltammetry > Peak Find, then choose Cyclic Voltammetry > Automatic Baseline. Vf (V vs. Ref) is the potential, and the Height (A) is the peak current. c. Repeat for both cathodic and anodic peaks. d. Fill in the appropriate column in the table below. 3. Repeat step 2 for all the other scan rates. Scan Rate (mv/s) E pc (mv) E pa (mv) I pc (µa) I pa (µa) Print graphs. 1. Print a graph of the ten different scan-rates overlaid onto one plot. a. Open the FeCN6 1000mVs-1.DTA file. b. Choose File > Overlay. c. Select the other graphs to be overlaid. d. Print the complete plot. Sample data

29 52 Cyclic Voltammetry Typical plot e. Include this plot in your laboratory report. 2. Using software designated by your laboratory instructor, create plots of i pc versus scan rate 1/2, and i pa versus scan rate 1/2. 3. Print these two plots. Sample data Sample data 4. Include these two plots in your laboratory report. Calculate your results. 1. From your scan-rate data, calculate ΔE p, E 1/2, and i pc /i pa, then fill in the table below with your results. Scan Rate (mv/s) ΔE p (mv) Gamry Instruments, Inc.

30 Questions 53 E 1/2 (mv) i pc /i pa From the plots of the i p versus scan rate 1/2, determine the slope of the best-fitting line. a. Slope of the graph i pc versus scan rate 1/2 = 38.0 b. Slope of the graph i pa versus scan rate 1/2 = Using the Randles-Ševćik equation and the slope from the graph of i pc versus scan rate 1/2, calculate the diffusion coefficient for potassium ferricyanide. Use the Randles-Ševćik equation, nf D ip = o nFAC RT Square both sides and rearrange to solve for D: 2 irt p D = ] g nfaco Substitute in the appropriate values with units: ] 38. # 10 Ag $ JK mol $ 298 K D = mol -1 ] g ] 1g ] Cmol g ] cm g b 2# 10 3 l ] 1 Vs g cm D = cm 2 /s XXQuestions 1. Based on the Randles-Ševćik equation, would you expect the peak current to increase or decrease as the temperature increases? Why? As the temperature increases, the diffusion coefficient would increase, because as the temperature increases the square root increases because T is in the denominator of the fraction in the square root. Also, as the temperature increases there is an increase in molecular kinetic energy and thus an increase in the diffusion rate. 2. The average distance that molecules move in solution is expressed by the formula l = 2Dt where l is distance (cm), Answers to questions

31 54 Cyclic Voltammetry D is diffusion coefficient (S m 2 /s), and t is time (s). Using your calculated diffusion coefficient, how long would it take for the analyte to diffuse 1 mm? t = l = = -5 = D 658 s = 11 min 2 ] 2g] 76. # 10 g 152. # (Bonus question) Calculate the ratio of slopes i pc and i pa. Based on this number, is the reaction of ferricyanide reversible, pseudo-reversible, or non-reversible? Why? The ratio will be close to 1, but should be just below 1. This indicates a reversible reaction, because all of the species that were reduced are being oxidized in the back reaction. The ratio should be just below 1 because some of the reduced species will have diffused away from the face of the electrode and thus were not electrolyzed. XXCommon Problems Instrument banana plugs connected to the incorrect jacks on the SPE board. This is a fatal error, resulting in data that will not be appropriate for analysis. Incorrect potentials input into the software for the scan. The usability of these data for analysis will depend upon the potentials that were entered and the shape of the voltammogram. If the peaks for both the forward and reverse scans are clearly visible in the potential window used, then the data are sufficient for analysis. If the peaks are not present, then the solution will have to be rerun. Gamry Instruments, Inc.

32 Goals 173 Electrochemical Impedance Spectroscopy XXGoals To learn the effect of placing capacitors and resistors in series and parallel To model electrochemical impedance spectroscopy data XXExperimental Apparatus Gamry Instruments Interface 1000T potentiostat Gamry Instruments Framework software package installed on a host computer Gamry Instruments AC Dummy Cell (Gamry part number ) Two 2.7 V, 3 F capacitors 20 Ω, ¼ W (or higher power-rating) resistor 100 Ω, ¼ W (or higher power-rating) resistor XXBackground Electrochemical impedance spectroscopy (EIS) is a popular method for studying an electrochemical interface. EIS is a two-part technique, that is: First, the electrical response of the electrochemical interface is recorded when a small alternating current (AC) potential is applied, and Second, the data are fitted to a theoretical electronic circuit that is designed to be equivalent to the actual system. In the first part (applying AC to the sample), the system is immersed in electrolyte, and an AC potential is applied, with the AC frequency carefully stepped from a high frequency (1 MHz or more) down to a low frequency (~1 Hz or less), usually in a logarithmic sequence. While perfect resistors respond without delay or loss in amplitude to AC input, all real electrical components (including surfaces undergoing corrosion) respond to such AC with a loss in amplitude, and a slight delay in time (phase-shift). How the electrochemical system responds to the AC input reveals much about the internal physical and chemical structure of the system. Therefore we cannot use the ideal Ohm s Law equation to describe our electrochemical surface, R = E I

33 174 Electrochemical Impedance Spectroscopy where R is the resistance of the system, E is the potential applied to the system, and I is the current applied to the system. Instead, we must consider the actual phase-shifted response of the system to the applied potential. Now we can describe the AC excitation potential applied to the system as a sine wave: E = E0 sin] ~ tg where E is the applied potential as before, E 0 is the AC amplitude, t is time, and ω is radial frequency (and ω = 2πf). The electrochemical system s response (Figure 10.1), then, is I = I0 sin^~ t + ] h where the phase-shift away from the applied AC is ϕ. The amplitude of the excitation signal is kept small so that the cell s response is pseudo-linear. In a pseudo-linear system the cell s frequency response is the same frequency as the excitation signal. Figure An applied AC potential (upper graph); a system s response is shifted in phase and amplitude (lower graph). Gamry Instruments, Inc.

34 Background 175 We cannot use the term resistance to describe the electrochemical system s ability to resist current flow because we are not operating under the conditions of an ideal resistor. Instead we must introduce the term impedance with symbol Z, analogous to an electrical inductor or coil of wire. The impedance can be described using complex numbers as: Z] ~ g = Z0 ^cos] + j sin ] h where j is imaginary. Note that this expression has a real component (cosϕ) and an imaginary component (jsinϕ). If we plot the real part on the x-axis, and the imaginary part on the y-axis, we create a Nyquist plot (Figure 10.2). The term impedance was invented by physicist-mathematician-electrical engineer Oliver Heaviside ( ) in The Nyquist plot was named for the electrical engineer Harry Nyquist ( ). Figure Typical Nyquist plot. In a Nyquist plot, the absolute value of the impedance Z is the length of the vector. The angle between the vector and the x-axis is referred to as the phase angle ϕ (or often ω). A problem with Nyquist plots is that the frequency used for each point on the curve is not determinable. Therefore another popular plotting scheme is the Bode (pronounced BOH-dee ) plot, which incorporates two distinct curves, usually plotted separately but sometimes overlaid (Figure 10.3 shows both styles). The x-axis is log(frequency, f). The y-axis uses the logarithm of the absolute values of the impedance ( Z =Z 0 ) for the impedance curve, and the phase-shift (plotted on a linear scale) for the phase-shift curve. An impedance experiment can be run in two ways: galvanostatic or potentiostatic. In a potentiostatic EIS experiment the amplitude of the applied voltage for a sinusoidal wave is controlled, and the current response of the system from that signal is measured. In a galvanostatic EIS experiment the amplitude of the applied current for a sinusoidal wave is controlled, and the potential response of the system from that signal is measured. When you choose the appropriate technique, The Bode plot was invented by the electrical engineer and inventor Hendrik Bode ( ).

35 176 Electrochemical Impedance Spectroscopy Figure Typical Bode plot styles. On the left shows stacked graphs, with the upper graph is log Z vs. log(frequency) and lower graph is phase-shift vs. log(frequency). Below is an overlaid mode, with log Z and phase-shift both plotted against log(frequency). the general rule of thumb is to control the smaller signal and measure the larger signal, so that experimental noise is reduced. Typically that means that you choose potentiostat EIS; however in today s experiment we are using galvanostatic EIS because the current response of the systems under study are small. The second part of EIS is the analysis of a Nyquist or Bode plot. Here the researcher starts with a hypothetical electrical-circuit model composed of networks of resistors, capacitors, and other elements. The model is used to mathematically calculate the response of this network, and that response is compared to the experimental data taken. The researcher then tries to explain the physical or chemical rationale behind each circuit element in the model equivalent circuit. Each component of the electrical circuit model must have a corresponding real element. This means that elements are not added to the model unless they can be physically explained, even if adding elements produces a model that statistically fits to the data better. Some circuit elements are: Solution resistance (the resistance that the ions in solution offer to a current), Double-layer capacitance (the capacitance that adsorbed ions create when sitting on a conductive surface), Polarization resistance (the resistance generated by electrochemical reactions at an electrode surface), and Gamry Instruments, Inc.

36 Procedure 177 Coating capacitance (when an insulating coating such as paint sets up a capacitance between the electrolyte solution and underlying metal). Many other physico-chemical circuit elements exist. There are quite a few models for equivalent circuits; this text does not have sufficient space to treat them in detail. You can imagine various electrical scenarios, especially with corroding or rusting metals covered by a failing protective coating perforated with holes and pores. Hence EIS is a common technique for studying and modeling the behavior of corroding metallic surfaces, especially when covered by a layer of paint. In today s experiment you examine two elements of a cell model in the form of capacitors and resistors. You will also evaluate and analyze a traditional Randles cell. The Randles model was first described by electrochemist John Edward Brough Randles ( ) in XXProcedure 1. Turn on the potentiostat. 2. Open the Gamry Framework software on the host computer. 3. Take capacitor measurements. a. Prepare the first capacitor for testing by connecting the green (working) and blue (working sense) alligator clips to the negative lead on the capacitor. Connect the red (counter), orange (counter sense), and white (reference) alligator clips to the other lead of the capacitor. Single capacitor attached to potentiostat. NOTE: Be sure of the proper polarity. Improper connections can damage the capacitor. b. When the Framework registers that the potentiostat is connected to the host computer, charge the capacitor: Go to Experiment > Physical Electrochemistry > Chronopotentiometry. Set the parameters equal to those found in Figure c. Run the experiment. d. After the experiment ends, go to Experiment > Electrochemical Impedance > Galvanostatic EIS. Set the parameters Lab Book with SPE teacher.indd 177 Capacitors in parallel attached to potentiostat. 12/13/ :23:59 AM

37 178 Electrochemical Impedance Spectroscopy Figure Experiment set-up window for chronopotentiometry. equal to those found in Figure e. Run the second experiment. f. Repeat steps 3(a) (e) for the second capacitor, making sure to change the Output File name from Capacitor 1 to Capacitor 2. g. Connect the capacitors in parallel, making sure that both capacitors are ori- Gamry Instruments, Inc.

38 Procedure 179 Figure Experiment set-up window for galvanostatic EIS. ented in the same direction, and repeat steps 3(a) (e), changing the Output File name to Capacitors in parallel. NOTE: To ensure proper contact between both capacitors and the alligator clips, twist the leads of the capacitors together prior to attaching the clips. h. Connect the capacitors in series, making sure that both capacitors are oriented in the same direction, and repeat steps 3(a) (e), changing the Output File name to Capacitors in Series. Capacitors in series attached to potentiostat. 4. Take resistor measurements. a. Prepare the 20 Ω resistor for testing by connecting the green (working) and blue (working sense) alligator clips to one lead of the resistor. Connect the red (counter), orange (counter sense), and white (reference) alligator clips Lab Book with SPE teacher.indd /13/ :24:03 AM

39 180 Electrochemical Impedance Spectroscopy to the other lead of the resistor. b. Resistors do not need to be charged, so chronopotentiometry is unnecessary. Go to Experiment > Electrochemical Impedance > Galvanostatic EIS. Set the parameters equal to those found in Figure c. Run the experiment. d. Repeat steps 4(a) (c) for the 100 Ω resistor, making sure to change the Output File name from Resistor 1 to Resistor 2. Single resistor attached to potentiostat. e. Connect the resistors in parallel, and repeat steps 4(a) (c), changing the Output File name to Resistors in parallel. f. Connect the resistors in series, and repeat steps 4(a) (c), changing the Output File name to Resistors in series. 5. Measure the EIS Dummy Cell as a Randles cell. a. Connect the potentiostat to the EIS Dummy Cell side of the AC Dummy Cell as per Figure (The AC Dummy Cell acts as a very good Randles cell.) Figure Connections from the Universal Dummy Cell (EIS Dummy Cell side) to the potentiostat. Gamry Instruments, Inc. Lab Book with SPE teacher.indd /13/ :24:09 AM

40 Reference 181 NOTE: Do not let the various alligator clips touch each other. b. The AC Dummy cell does not need to be charged, so chronopotentiometry is unnecessary. Go to Experiment > Electrochemical Impedance > Potentiostatic EIS. Set the parameters equal to those found in Figure Figure Experiment set-up window for potentiostatic EIS on a Randles cell. c. Run the experiment. 6. After all experimental runs are complete, turn off the potentiostat. Copy or move the data that you obtained today from the folder C:\Users\Public\Documents\My Gamry Data to your portable storage device for later analysis. XXReference Barsoukov, E. and Macdonald, J.R., eds., Impedance Spectroscopy: Theory, Experiment, and Applications, 2 nd ed., Hoboken, NJ: John Wiley & Sons, 2005.

41 182 Electrochemical Impedance Spectroscopy Gamry Instruments, Inc.

42 Data Analysis 183 XXData Analysis 1. Open Gamry Echem Analyst Software. 2. Use Echem Analyst to determine the capacitance of the capacitors. a. Open the Capacitor 1 data file. b. Create the appropriate electronic model circuit. Choose Galvanostatic Impedance > Model Editor. In the model editor window, open the Fuel Cell.MDL model. Right-click on the two constant-phase elements ( ) and delete them. Then click on the capacitor icon at the top ( ) two of these are needed and place them where the constant-phase elements were. Draw this model below, and save this file as capacitors.mdl. Close the model editor. capacitors.mdl Model Students answers c. In the Echem Analyst software, proceed to Galvanostatic Impedance > Fit a Model (Simplex Method), and select the capacitors.mdl model you just created. A new window opens containing all of the circuit elements from the model. Click the AutoFit button and the model runs. d. After the Impedance Fit by the Simplex Method window displays that the model has completed its simulation, record the total value of both capacitor values in the table in the Results section. e. Open the other capacitor data files, and repeat steps 2(b) (d) for each. f. Using the known values of the capacitors from your laboratory instructor, calculate the total capacitance of the capacitors in series and parallel, also recording them in the same table. 3. Use Echem Analyst to determine the resistance of the resistors. a. Open the Resistor 1 data file. The resistor model is already created in the software. View and draw the model below by going to Galvanostatic Impedance > Model Editor, and opening the R.MDL model.

43 184 Electrochemical Impedance Spectroscopy R.MDL Model b. In the Analyst software, proceed to Galvanostatic Impedance > Fit a Model (Simplex Method) and select the R.MDL model you just created. A new window opens containing the circuit element from the model. Click the AutoFit button and the model runs. c. After the Impedance Fit by the Simplex Method window displays that the model has completed its simulation, record the total value of the two resistors and capacitor values within the table in the Results section. d. Open the other resistor data files and repeat steps 3(b) and (c) for each. e. Using the known values of the resistors from your laboratory instructor, calculate the total resistance of the resistors in series and parallel, also recording them in the same table. 4. Use Echem Analyst to determine the resistance and capacitor values of the Randles cell. a. Open the Randles cell data file. The resistor model is already created in the software. View and draw the model below by going to Galvanostatic Impedance > Model Editor. and opening randles.mdl model. randles.mdl Model b. In the Analyst software proceed to Galvanostatic Impedance > Fit a Model (Simplex Method), and select the randles.mdl model you just created. A Gamry Instruments, Inc.

44 Data Analysis 185 new window opens containing the circuit element from the model. Click the AutoFit button and the model runs. c. After the Impedance Fit by the Simplex Method window displays that the model has completed its simulation, record the total value of both capacitor values within the table in the Results section of the lab. d. Calculate resistance Ru and resistance Rp of the Randles cell. From the Nyquist plot the Ru is the associated shift in the time constant from 0 Ω, while the Rp is the diameter of the semicircle created by the RC time constant. e. Calculate capacitance Cf. To calculate the capacitance from the Bode tab, change the y 2 -axis from Zphz to Zimag. This graphs the imaginary impedance versus the frequency. Record the frequency at which the maximum negative imaginary impedance occurs. Zimag: 1776 Ω Frequency: Hz Using this frequency, calculate the radial frequency. [Remember that ω(max) = 2πƒ] ω(max)=2πf ω(max)=2π(49.87 Hz) ω(max)=313.3 Hz Radial frequency: Hz The capacitance can now be calculated from the radial frequency, given that τ = RC = 1/ω(max). Record the calculated value in the Randles cell table in the Results section. (The R value is the one that you calculated from the semicircle created by the RC time constant.) RC = 1 ~ ( max) C = 1 R~ ( max) C = 1 ] 3000 X g] Hz g C = µf

45 186 Electrochemical Impedance Spectroscopy XXResults Capacitors: Model Total Capacitance (F) Capacitor Capacitor Capacitors in parallel Capacitors in series Resistors: Model Total Resistance (Ω) Calculated Total Capacitance (F) Calculated Total Resistance (Ω) Resistor Resistor Resistors in parallel Resistors in series Randles Cell: Circuit Element Model Values Calculated Values Resistance Ru Ω Ω Resistance Rp 3013 Ω 3013 Ω Capacitance Cf µf µf XXQuestions 1. Why is the amplitude of the excitation signal kept as small as possible in EIS? Analysis of a linear system is much simpler than a non-linear system. If the excitation signal is kept small, then the system is under a pseudo-linear response. If we measure outside of this pseudo-linear area, then the system s response will contain harmonics of the excitation signal. Gamry Instruments, Inc.

46 Common Problems How would the Nyquist and Bode plots change for the Randles cell measurement if a third resistor is added in series with the other circuit elements? Draw the circuit model with the extra resistor added. Students should draw one of the following two possibilities: If the resistor is added outside of the RC loop, then it would appear to the cell as additional solution resistance, and the semi-circle of the Nyquist plot would shift to higher resistances, but the radius would remain unchanged. In the Bode plot, the phase-angle data would decrease and shift to lower-frequency values, while the Zmod values at high frequencies would increase. If the resistor is added inside of the RC loop, then it would appear to the cell as additional polarization resistance, and the radius of the semi-circle would increase. In the Bode plot, the phase-angle data would increase and shift slightly to lower-frequency values, while the Zmod values at lower frequencies would increase. 3. All elements of the model must have a physical representation for the model to be valid, e.g., electrolyte solution, coating, porosity, working electrode face. What do the circuit elements of the Randles cell represent? Ru: Solution resistance. Rp: Polarization resistance of the electrode caused by the potential at the surface not being equal to the open-circuit potential. Cf: Double-layer capacitance at the surface of the electrode. 4. (Bonus Question) What would the Nyquist plot look like if a second RC loop (a capacitor-resistor pair in parallel) were added in series to the Randles Cell? A second semicircle would appear on the plot, if its RC time constant is different from the original, otherwise it would convolute with the original time constant and may be hard to distinguish. XXCommon Problems Not charging the capacitors prior to EIS measurements. Not having a good connection between the capacitors or resistors when twisting them into series and parallel configurations. This will be evident from noise in the data. Secure the connections and rerun the experimental setup.